A branch-and-cut algorithm for the k-edge connected subgraph problem

• Published in: Networks Vol. 55; no. 1; pp. 13 - 32
• Main Authors: Bendali, F., Diarrassouba, I., Mahjoub, A.R., Didi Biha, M., Mailfert, J.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01-01-2010; Wiley
• Subjects: Applied sciences; branch-and-cut; Computer Science; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Discrete Mathematics; Exact sciences and technology; facet; Information retrieval. Graph; k-edge connected graph; Operations Research; polytope; reduction operations; separation; Software; Theoretical computing; Polytope; Polyhedron; Edge(graph); branch-and-cut; Graph connectivity; Branch and cut method; separation; Subgraph; Connected graph; reduction operations; k-edge connected graph; facet; polytope
• ISSN: 0028-3045; 1097-0037
• DOI: 10.1002/net.20310

In this article, we consider the k‐edge connected subgraph problem from a polyhedral point of view. We introduce further classes of valid inequalities for the associated polytope and describe sufficient conditions for these inequalities to be facet defining. We also devise separation routines for these inequalities and discuss some reduction operations that can be used in a preprocessing phase for the separation. Using these results, we develop a Branch‐and‐Cut algorithm and present some computational results. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010